| Exam Board | OCR |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2010 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Binomial Theorem (positive integer n) |
| Type | Substitution into binomial expansion |
| Difficulty | Moderate -0.8 This is a straightforward binomial expansion question requiring routine application of the binomial theorem formula, followed by a simple substitution. Part (i) is mechanical calculation with no problem-solving, and part (ii) requires only recognizing that substituting x = w²/4 means the x³ term becomes the w⁶ term. Both parts are below average difficulty for A-level, being standard textbook exercises with clear methods. |
| Spec | 1.04a Binomial expansion: (a+b)^n for positive integer n1.04b Binomial probabilities: link to binomial expansion |
3 (i) Find and simplify the first four terms in the expansion of $( 2 - x ) ^ { 7 }$ in ascending powers of $x$.\\
(ii) Hence find the coefficient of $w ^ { 6 }$ in the expansion of $\left( 2 - \frac { 1 } { 4 } w ^ { 2 } \right) ^ { 7 }$.
\hfill \mbox{\textit{OCR C2 2010 Q3 [6]}}